What causes these black streaks along certain (concave?) edges?
You need to recalculate the normals of your mesh.
go in edit mode with TAB
select all with A 1 time, or 2 times, or 3 times (depending on if something is selected and if you're using 2.79 or 2.8)
- If you're using 2.79 or earlier, use Ctrl+N (recalculate outside) or Shift+Ctrl+N (recalculate inside)
- If you're using 2.8, Shift+N (recalculate outside) or Shift+Ctrl+N (recalculate inside)